Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

The current Australian Curriculum mandates that technology be utilised to support students to "investigate, create and communicate mathematical ideas and concepts" (ACARA, 2018). However, research reports suggest that use of digital technologies in Australian primary mathematics often focuses on the lower-order drilling of algorithms and…

In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…

This article looks at a simple geometry problem that also involves some reasoning about number combinations, and show how it was used in a Year 7 classroom. The problem is accessible to students with a wide range of abilities, and provides scope for stimulating extensive discussion and reasoning in the classroom, as well as an opportunity for…

This book focuses on integrity throughout the PhD journey and beyond, and is organised around two main themes: (1) integrity in relation to the capabilities developed by doctoral candidates for professional practice; and (2) integrity and coherence at the PhD system level. The working methods of key participants such as PhD candidates,…

This article reviews the famous "matching problem," with a particular focus on the expected number of objects that are correctly placed. The author discusses the following topics: three versions suitable for teaching the matching problem in the classroom; the solution to the matching problem; the use of the strong form of mathematical…

Teaching students to use and interpret representations in science is critically important if they are to become scientifically literate and learn how to communicate their understandings and learning in science. This study involved 248 students (119 boys and 129 girls) from 26 grade 6 teachers' classes in nine primary schools in Brisbane,…

The study reports on the types of questioning strategies teachers use to promote thinking, problem-solving and reasoning during small group discussions. The study also reports on the types of discourses students use to problem-solve and reason during their small group discussions. An audiotape of one class lesson from the three teachers included…

A problem given in the Australian Mathematics Competition for the Westpac Awards was stated as follows: With how many zeros does 2008! end? In this article, the author solves this problem, and provides further discussion on the related problems. These problems form a good model that helps students develop a logical thinking process toward problem…

It is important for students to develop critical thinking and other higher-order thinking skills during their tertiary studies. Along with the ability to think critically comes the need to develop students' meta-cognitive skills. These abilities work together to enable students to control, monitor, and regulate their own cognitive processes and…

Uses case studies to explore the pedagogical reasoning ability of second-year preservice primary teachers. Reports that the framework provided in a problem-based science education course enabled the teachers to refine their reasoning ability and to integrate their science knowledge, curriculum knowledge, and knowledge of learners. (Author/JRH)

Explores aspects of information retrieval skills such as end user training, indexing, controlled vocabulary systems, search protocol, boolean logic, problem analysis, and decision making. Suggests techniques for classroom instruction using simulations of online databases, CD-ROMs, and DIALOG's classroom instruction program. Describes several…

Found grades in science achieved by tenth-grade general science students correlated with their scores on Propositional Logic Test. The students' ability level was consistently related to the pattern of errors they committed on that measure. Mean scores were lowest on a subtest of ability to use the bicondition and implication, higher on the…